Existence and multiplicity of homoclinic orbits for second order Hamiltonian systems without (AR) condition

2011 ◽  
Vol 15 (1) ◽  
pp. 255-271 ◽  
Author(s):  
Li-Li Wan ◽  
◽  
Chun-Lei Tang
Keyword(s):  
Hamiltonian Systems ◽  
Homoclinic Orbits ◽  
Second Order ◽  
Existence And Multiplicity ◽  
Second Order Hamiltonian Systems

scholarly journals Existence and Multiplicity of Homoclinic Orbits for Second-Order Hamiltonian Systems with Superquadratic Potential

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Ying Lv ◽  
Chun-Lei Tang
Keyword(s):  
Hamiltonian Systems ◽  
Mountain Pass Theorem ◽  
Homoclinic Orbits ◽  
Second Order ◽  
Mountain Pass ◽  
Fountain Theorem ◽  
Existence And Multiplicity ◽  
Second Order Hamiltonian Systems ◽  
Superquadratic Potential

We investigate the existence and multiplicity of homoclinic orbits for second-order Hamiltonian systems with local superquadratic potential by using the Mountain Pass Theorem and the Fountain Theorem, respectively.

scholarly journals Homoclinic Orbits for Second-Order Hamiltonian Systems with Some Twist Condition

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Qi Wang ◽  
Qingye Zhang
Keyword(s):  
Hamiltonian Systems ◽  
Linear Growth ◽  
Homoclinic Orbits ◽  
Positive Definite ◽  
Second Order ◽  
Existence And Multiplicity ◽  
Second Order Hamiltonian Systems ◽  
Twist Condition

We study the existence and multiplicity of homoclinic orbits for second-order Hamiltonian systemsq¨−L(t)q+∇qW(t,q)=0, whereL(t)is unnecessarily positive definite for allt∈ℝ, and∇qW(t,q)is of at most linear growth and satisfies some twist condition between the origin and the infinity.

scholarly journals Homoclinic Orbits for a Class of Subquadratic Second Order Hamiltonian Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Li-Li Wan
Keyword(s):  
Hamiltonian Systems ◽  
Homoclinic Orbits ◽  
Second Order ◽  
Existence And Multiplicity ◽  
Second Order Hamiltonian Systems

The existence and multiplicity of homoclinic orbits are considered for a class of subquadratic second order Hamiltonian systems q¨t-Ltqt+∇Wt,qt=0. Recent results from the literature are generalized and significantly improved. Examples are also given in this paper to illustrate our main results.

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